Lectures related to Algebraic surface

Real Surfaces: Defects and Reconstructions

Explores the difference between ideal and real surfaces, defects, and surface reconstructions.

Ruled Surfaces: Generators and Applications

Explores ruled surfaces, surfaces generated by moving lines in space, including cones, cylinders, and hyperboloids, with applications in architecture.

Quadratic Surfaces in 3D Space

Explores quadratic surfaces in 3D space, discussing hyperboloids and their Cartesian equations, emphasizing the importance of reference frames.

Descriptive Geometry: Cones and Cylinders

Explains the definitions of cones and cylinders as ruled surfaces and how to find tangent planes to them.

Surface Geometry: Geodesics and Surface Area

Explores geodesics and surface area calculation for rotationally symmetric surfaces.

Mild Dissipative Surface Dynamics

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.

Properties of Cross Product: Algebraic Aspects

Explores the algebraic properties of the cross product and its linearity.

Curve of Genus 2: Very Ample Divisors

Explores very ample divisors on curves of genus 2 and their implications.

Real Surfaces: Line Defects

Explores line defects in real surfaces and their influence on surface energy.

Algebraic Cycles and Etale Cohomology

Explores algebraic cycles, etale cohomology, and counterexamples to the Hodge conjecture.

Descriptive Geometry: Cones and Cylinders

Covers the definitions and characteristics of cones and cylinders as ruled surfaces with generating lines.

Surfaces with Variable Curvature

Explores surfaces with variable curvature, discussing their construction and properties.

Surface Classification

Covers the classification of surfaces using polygonal presentations and homeomorphism.

Adjunctions and Applications

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Geometric Surfaces: Paraboloid and Hyperboloid Concepts

Covers the geometric properties of hyperbolic paraboloids and hyperboloids, focusing on their construction and curvature characteristics.

Principal Curvatures: Gaussian Curvature

Explores principal curvatures and Gaussian curvature in the context of minimal surfaces, demonstrating their real-world applications.

Unique Ergodicity for Generic Foliations

Explores unique ergodicity for generic foliations on Kähler surfaces.

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Abstract algebra and type classes

Covers abstract algebra concepts using type classes in Scala, including defining monoids, generalizing reduce functions, and typeclass laws.